CFDP 1951

If the historical average annual real interest rate is m > 0, and if the world is stationary, should consumption in the distant future be discounted at the rate of m per year? Suppose the annual real interest rate r(t) reverts to m according to the Ornstein Uhlenbeck (OU) continuous time process dr(t) = α[m – r(t)]dt + kdw(t), where w is a standard Wiener process. Then we prove that the long run rate of interest is r∞ = m – k2/2α2. This conﬁrms the Weitzman-Gollier principle that the volatility and the persistence of interest rates lower long run discounting. We ﬁt the OU model to historical data across 14 countries covering 87 to 318 years and estimate the average short rate m and the long run rate r∞ for each country. The data corroborate that, when doing cost beneﬁt analysis, the long run rate of discount should be taken to be substantially less than the average short run rate observed over a very long history.